Beyond the Wisdom of the Crowd: How Network Topology Distorts Collective Perception

TL;DR

This work shows that network topology can induce systematic misperceptions of population-level attributes even when individuals are unbiased. By modeling a two-community population with a DeGroot-style message-passing process on a stochastic block model, it derives a closed-form stationary perception $\mu_{\infty}$ that depends on community sizes, internal degrees, and cross-connections: $\mu_{\infty}=\frac{N_+ k_+ - N_- k_-}{N_+ k_+ + N_- k_- + 4 N_+ N_- p}$. The authors validate the theory against real survey data from three countries, showing the network-aware estimator $\hat{\mu}_{\infty}$ better predicts observed perceptions than simply using social-circle estimates. The results highlight implications for addressing echo chambers, segregation, and polarisation, and suggest policy directions to mitigate topology-driven biases in collective judgments and forecasts.

Abstract

Cognitive biases are often attributed to heuristics or limited information. Yet the structure of social networks is a key, often-overlooked source of perceptual bias. When information passes through social connections, the network alone can systematically distort how individuals view society. We use a simple model in which agents have a binary attribute (e.g., atheist or believer) and show that network topology alone can cause misperceptions of peers' attributes. These misperceptions persist even after aggregation and challenge the idea of the "wisdom of the crowd." We derive an estimator that predicts the size and direction of these biases from network features. We validate our findings using three large-scale opinion surveys. Our results show that network structure is a critical factor in collective perception, with major implications for reducing segregation, polarisation, and the marginalisation of minorities.

Figures (6)

• Figure 1: Visual representation of the message-passing algorithm. (1a) The simple graphs in the first row show how perception forms for one user at the centre and their social connections. At $d=0$, nodes do not know about others, so each only knows its own attribute: $\mu_i(0)=s_i$ ($+1$: green, $-1$: purple). (1b) At $d=1$, each user shares their own attribute with their nearest neighbours, resulting in a revised perception of the attribute balance in the network (indicated by the composite user colour between green and purple). As this process is iterated over greater distances, each user continues to receive messages from neighbours, enabling the focal user to obtain information from nodes farther within the network. (1c) After $d=5$ iterations, the user has received messages from peers up to five steps away. (1d) At $d=30$, the user attains a stable perception of the average attribute in the network. (1e) The second row shows the process for the whole network, using a stochastic block model (SBM) with $N=100$, $m=0$, $k_+=5$, $k_-=10$, and $p=0.01$. At $d=0$, no propagation has occurred, so each node's perception corresponds to its own attribute. (1f) At $d=1$, each node only gets messages from its neighbours, and nodes with neighbours in both communities develop a milder perception of the mean attribute. (1g) At $d=5$, signals have reached nearly all nodes in the network. (1h) At $d=30$, perceptions get close to stable values, which are not the same as m (the final average is $-0.26$, not $0$), challenging the idea of the wisdom of the crowd. This happens because $-1$ nodes have more connections, so they share their views more widely.
• Figure 2: Message passing simulations in four different scenarios. Plots on the right column show the mean attribute $m$ (continuous line) and the stationary perception $\mu_\infty$ (dashed line), while symbols represent the mean perception of the whole network ${\mu}$ and the mean perception within each community ${\mu}_{\pm}$ as a function of distance $d$. The perception bias is given by the difference between $m$ and $\mu(d)$ for $d\to\infty$. All graphs on the left are merely illustrative of the real ones on which the simulations were run. (2a) SBM with same community size ($N_+=N_-$), small mixing (low $p$) and different internal degrees $k_+\neq k_-$; (2b) SBM with different community size ($N_+\neq N_-$), small mixing (low $p$) and same internal degrees $k_+= k_-$; (2c) SBM with equal community size ($N_+=N_-$), high mixing (high $p$) and same internal degrees $k_+= k_-$. (2d) Karate club graph with affiliation attributes. Here, the dotted line is the stationary perception computed with heterogeneous mean-field approximation, i.e., accounting for degree correlations in the real network.
• Figure 3: Assessment of the perception bias estimators. (3a) Sample illustration of survey data. For each user, country, and issue, the answers include her attribute $x_i$, her social circle $y_i$, and her country-level perception $z_i$. (3b-d) Error of the social circle estimator $\hat{\mu}_1$ and the message-passing estimator $\hat{\mu}_\infty$ in predicting the average perception $\hat{\mu}$ in the surveys, for the three countries in the data. The error bars account for one standard deviation of the estimator. Values are reported after the Fisher z-transform, and issues are ordered by message-passing error.
• Figure S1: Stationary state in simulations vs. theoretical solution. The plots compare the average perception of the mean attribute $\mu$ reached in the simulations and compare them with the theoretical solution, as a function of $m$ and different values of $p$, both for $k_+=k_-$ (S1a) and $k_+ \neq k_-$ (S1b). The points for the simulations are averaged on $10$ runs each.
• Figure S2: Simulations with Label Propagation on SBM and Karate Club network 2a) SBM with same community size but different connectivity of communities; 2b) SBM with same connectivity but different community size; 2c) SBM with same community size and connectivity with high mixing (low polarization); 2d) Karate club graph with affiliation attribute. The plots show no significant difference with the simulations with DeGroot model, except for the evolution being faster with label propagation.